A local bank lends $12,000 using a 150-day 9% simple interest note that was signed on May 18. The bank later sells the note at a discount of 14% on July 5. Find (a) the discount, (b) the proceeds, and (c) the amount of money the bank gains or loses.

A local bank lends $12,000 using a 150-day 9% simple interest note that was signed on May 18. The bank later sells the note at a discount of 14% on July 5. Find (a) the discount, (b) the proceeds, and (c) the amount of money the bank gains or loses

To find the answers to this question, we need to calculate the discount, proceeds, and gain/loss of the bank using the given information. Let's break it down step by step.

Step 1: Calculate the interest payable.
Interest is calculated using the formula: Interest = Principal x Rate x Time.
In this case, the principal (P) is $12,000, the rate (R) is 9% (expressed as 0.09), and the time (T) is 150 days.

Interest = $12,000 x 0.09 x (150/365) [Converting days to years by dividing by 365]
= $438.36 (approximately)

Step 2: Calculate the maturity value.
Maturity value is calculated by adding the principal amount with interest.
Maturity Value = Principal + Interest
= $12,000 + $438.36
= $12,438.36

Step 3: Calculate the discount.
Discount is the difference between the maturity value and the selling price.
Discount = Maturity Value x Discount Rate
= $12,438.36 x 0.14 [Converting the discount rate to decimal]
= $1,733.17 (approximately)

Step 4: Calculate the proceeds.
Proceeds are the selling price of the note after applying the discount.
Proceeds = Maturity Value - Discount
= $12,438.36 - $1,733.17
= $10,705.19 (approximately)

Step 5: Calculate the gain/loss.
The gain/loss is the difference between the maturity value and the proceeds.
Gain/Loss = Maturity Value - Proceeds
= $12,438.36 - $10,705.19
= $1,733.17 (approximately)

Now let's summarize the answers:
(a) The discount is approximately $1,733.17.
(b) The proceeds are approximately $10,705.19.
(c) The bank gains or loses approximately $1,733.17. In this case, the bank loses this amount as the note was sold at a discount.